Measure Casting#
These combinators are used to cast the output measure of a Measurement.
Input Measure |
Output Measure |
Constructor |
|---|---|---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
opendp.combinators.make_approximate() is used for casting an output measure from MaxDivergence to Approximate<MaxDivergence>.
This is useful if you want to compose pure-DP measurements with approximate-DP measurements.
>>> input_space = dp.atom_domain(
... T=float, nan=False
... ), dp.absolute_distance(T=float)
>>> meas_pureDP = input_space >> dp.m.then_laplace(scale=10.0)
>>> # convert the output measure to `Approximate<MaxDivergence>`
>>> meas_fixed_approxDP = dp.c.make_approximate(meas_pureDP)
>>> # `Approximate<MaxDivergence>` distances are (ε, δ) tuples
>>> meas_fixed_approxDP.map(d_in=1.0)
(0.1, 0.0)
The combinator can also be used on measurements with a ZeroConcentratedDivergence privacy measure.
opendp.combinators.make_pureDP_to_zCDP() is used for casting an output measure from MaxDivergence to ZeroConcentratedDivergence.
opendp.combinators.make_zCDP_to_approxDP() is used for casting an output measure from ZeroConcentratedDivergence to SmoothedMaxDivergence.
>>> meas_zCDP = input_space >> dp.m.then_gaussian(scale=0.5)
>>> # convert the output measure to `SmoothedMaxDivergence`
>>> meas_approxDP = dp.c.make_zCDP_to_approxDP(meas_zCDP)
>>> # SmoothedMaxDivergence distances are privacy profiles (ε(δ) curves)
>>> profile = meas_approxDP.map(d_in=1.0)
>>> profile.epsilon(delta=1e-6)
11.688596249354896
opendp.combinators.make_fix_delta() changes the output measure from SmoothedMaxDivergence to Approximate<MaxDivergence>.
It fixes the delta parameter in the curve, so that the resulting measurement can be composed with other Approximate<MaxDivergence> measurements.
>>> # convert the output measure to `FixedSmoothedMaxDivergence`
>>> meas_fixed_approxDP = dp.c.make_fix_delta(
... meas_approxDP, delta=1e-8
... )
>>> # FixedSmoothedMaxDivergence distances are (ε, δ) tuples
>>> meas_fixed_approxDP.map(d_in=1.0)
(13.3861046488579, 1e-08)
These last two combinators allow you to convert output distances in terms of ρ-zCDP to ε(δ)-approxDP, and then to (ε, δ)-approxDP.